A rail gun consists of two parallel guide rails that are connected to a power supply. When a conductive projectile is placed on the rails, a magnetic field is created that is perpendicular to the rails. As a result, a Lorentz force is created that accelerates the projectile at a rate proportional to the current squared.

The Lorentz force states that a charged particle that moves in the presence of an electric or magnetic field will experience a force of the form:

where \begin{align*}q\end{align*} is the charge of the particle, \begin{align*}v\end{align*} is the particle's velocity, and \begin{align*}E\end{align*} and \begin{align*}B\end{align*} are the electric and magnetic fields respectively. For a rail gun to be effective, the power supply that is used must be able to deliver constant and sustained currents while firing the projectile. All the materials used must be extremely strong to withstand the large amount of current and friction forces involved.

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Using the information provided above, and the link below, answer the following questions.

If a charged particle has a velocity along the \begin{align*}x\end{align*}-axis, in what direction would the Lorentz force be if the particle enters a region with an electric field pointed along the \begin{align*}y\end{align*}-axis?

If a particle with zero charge has a velocity along the \begin{align*}x\end{align*}-axis, in what direction would the Lorentz force be if the particle enters a region with a magnetic field pointed along the \begin{align*}y\end{align*}-axis?

If the particle in the previous problem has a positive charge, in what direction would the Lorentz force be?